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With the start of the school year, educators are looking for instructional strategies that can be adapted for both in-person or virtual instruction at any moment due to the persistent and unpredictable school closures in responses to the COVID-19 pandemic. It is important that these strategies be able to meet every student's individual learning needs particularly as we consider potential learning losses as a result of school closures. Station rotation is one approach to promote personalized learning that policymakers or educators may want to consider implementing to meet students' individual learning needs. In this approach, teachers use technology and have flexibility in grouping students to provide differentiated instruction. Individual classrooms can use station rotation with minimal up-front investment and the model is flexible to work in a variety of classrooms. Station rotation may also be adapted to use with students during in-person and virtual instruction for schools considering hybrid or blended learning models in order to safely re-open in the fall. [For the full report, see ED610292.]

We revise the analysis of the bottomonium hyperfine splitting within the lattice nonrelativistic QCD. The Wilson coefficients of the radiatively improved lattice action are evaluated by a semianalytic approach based on the asymptotic expansion about the continuum limit. The nonrelativistic renormalization group is used to estimate the high-order radiative corrections. Our result for the $1S$ hyperfine splitting is $M_{\Upsilon(1S)}-M_{\eta_b(1S)}=52.9\pm 5.5~{\rm MeV}$. It reconciles the predictions of the continuum and lattice QCD and is in very good agreement with the most accurate experimental measurement by Belle collaboration., Comment: 6 pages, 2 figures, journal version

We report on the development of a frequency modulatable 795 nm semiconductor laser based on self-injection locking to a high quality factor whispering gallery mode microresonator. The laser is characterized with residual amplitude modulation below -80 dB and frequency noise better than 300 Hz/Hz^(1/2) at offset frequencies ranging from 100 Hz to 10 MHz. The frequency modulation (FM) speed and span of the laser exceed 1 MHz and 4 GHz, respectively. Locking of the laser to Doppler-free saturated absorption resonance of 87Rb D1 line is demonstrated and frequency stability below 10^(-12) is measured for integration time spanning from 1 s to 1 day. The architecture demonstrated in this study is suitable for realization of frequency modulatable lasers at any wavelength., Comment: 9 pages, 5 figures

We demonstrate a free running 10GHz microresonator-based RF photonic hyper-parametric oscillator characterized with phase noise better than -60dBc/Hz at 10Hz, -90dBc/Hz at 100Hz, and -150dBc/Hz at 10MHz. The device consumes less than 25mW of optical power. A correlation between the frequency of the continuous wave laser pumping the nonlinear resonator and the generated RF frequency is confirmed. The performance of the device is compared with the performance of a standard optical fiber based coupled opto-electronic oscillator of OEwaves., Comment: 9 pages, 8 figures. Wei Liang at al., Proceedings of SPIE Vol. 8960 (SPIE, Bellingham, WA 2014), 896010

We discuss our recent progress in iimproving the phase noise of a semiconductor laser using self-injection locking of to a mode of a high-Q whispering gallery mode resonator. Locking efficiency is analyzed for semiconductor distributed feedback (DFB) as well as Fabry-Perot (FP) lasers operating at 690nm, 1060nm, 1550nm, and 2000nm. Instantaneous linewidth below 300 Hz is realized with telecom DFB lasers. Tunability of the lasers is demonstrated. Commercially available packaged "plug-and-play" devices are manufactured., Comment: 9 pages, 11 figures

Mechanical clocks consist of a pendulum and a clockwork that translates the pendulum period to displayed time. The most advanced clocks utilize optical transitions in atoms in place of the pendulum and an optical frequency comb generated by a femtosecond laser as the clockwork. The comb must be stabilized at two points along its frequency spectrum: one with a laser to lock a comb line to a transition in the atom, and another through self referencing to stabilize the frequency interval between the comb lines. This approach requires advanced techniques, so optical atomic clocks are currently laboratory devices in specialized labs. In this paper we leverage unique properties of Kerr comb oscillators for realization of optical atomic clocks in miniature form factors. In particular, we describe a clock based on D1 transition of 87Rb that fits in the palm of the hand, and can be further miniaturized to chip scale., Comment: 4 pages, 4 figures

We show that scattering-based interaction among nearly degenerate optical modes is the key factor in low threshold generation of Kerr frequency combs in nonlinear optical resonators possessing small group velocity dispersion (GVD). The mode interaction is capable of producing drastic change in the local GVD, resulting in either a significant reduction or increase of the oscillation threshold. It is also responsible for the majority of observed combs in resonators characterized with large normal GVD. We present results of our numerical simulations as well as supporting experimental data.

We report on realization of an efficient triply-resonant coupling between two long lived optical modes and a high frequency surface acoustic wave (SAW) mode of the same monolithic crystalline whispering gallery mode resonator. The coupling results in an opto-mechanical oscillation and generation of a monochromatic SAW. A strong nonlinear interaction of this mechanical mode with other equidistant SAW modes leads to mechanical hyper-parametric oscillation and generation of a SAW pulse train and associated frequency comb in the resonator. We visualized the comb observing the modulation of the modulated light escaping the resonator.

We demonstrate that whispering gallery mode resonators can be utilized to generate optical frequency combs based on four wave mixing process at virtually any frequency that lies in the transparency window of the resonator host material. We show theoretically how the morphology of the resonator can be engineered to produce a family of spectrally equidistant modes with anomalous group velocity dispersion appropriate for the comb generation. We present experimental results for a frequency comb centered at 794 nm to support our theoretical findings., Comment: 4 pages, 2 figures

We demonstrate a miniature self-injection locked DFB laser using resonant optical feedback from a high-Q crystalline whispering gallery mode resonator. The linewidth reduction factor is greater than 10,000, with resultant instantaneous linewidth less than 200 Hz. The minimal value of the Allan deviation for the laser frequency stability is 3x10^(-12) at the integration time of 20 us. The laser possesses excellent spectral purity and good long term stability., Comment: To be published in Optics Letters

We propose a method for frequency stabilization of a resonant opto-mechanical oscillator utilizing the different temperature and strain dependence of the optical and mechanical modes. In particular, we show that the temperature of the mechanical resonator can be stabilized to microKelvin level without the need for an external temperature or frequency reference. The method is promising for reaching the thermodynamically limited performance of opto-mechanical oscillators, and even for lifting the thermodynamic limit.

We report on the observation of a novel mode locked optical comb generated at the Raman offset (Raman comb) in an optically pumped crystalline whispering gallery mode resonator. Mode locking is confirmed via measurement of the radio-frequency beat note produced by the optical comb on a fast photodiode. Neither the conventional Kerr comb nor hyper-parametric oscillation is observed when the Raman comb is present.

We consider the currents formed by a heavy and a light quark within Quantum Chromodynamics and compute the matching to Heavy Quark Effective Theory to three-loop accuracy. As an application we obtain the third-order perturbative corrections to ratios of B-meson decay constants., Comment: 23 pages, full results are available as Mathematica files at http://www-ttp.particle.uni-karlsruhe.de/Progdata/ttp09/ttp09-41/ ; v2: an error in comparison with Ref. [8] fixed ; v3: Journal version

A surface acoustic wave (SAW) creates its own high-Q ultra-small volume whispering gallery modes (WGMs), different from usual bulk acoustic WGMs, in an optical dielectric WGM resonator. We show that it is possible to realize an externally controllable, efficient triply-resonant opto-mechanical interaction between two optical WGMs and the SAW WGM and to use such an interaction in various sensor applications.

We present the three-loop QCD corrections to the quark chromomagnetic moment including two different nonzero masses. This is a necessary ingredient to obtain the corresponding corrections to the chromomagnetic coefficient in the Heavy Quark Effective Theory (HQET) Lagrangian., Comment: 4 pages

We evaluate the corrections to the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to three-loop order containing a closed heavy-fermion loop. The result constitutes a building block both for the bottom- and top-quark system at threshold. Strong emphasis is put on our completely automated approach of the calculation including the generation of the Feynman diagrams, the identification of the topologies, the reduction to master integrals and the automated numerical computation of the latter., Comment: 14 pages

All three-loop on-shell QCD Feynman integrals with two masses can be reduced to 27 master integrals. Here we calculate these master integrals, expanded in epsilon, both exactly in the mass ratio and as series in limiting cases., Comment: 22 pages; complete results as Mathematica files are available at http://www-ttp.particle.uni-karlsruhe.de/Progdata/ttp09/ttp09-08/ v2: 2 references added, v3: Ref. [16] corrected

Some fundamental and formal aspects of the quantum dwell time are reviewed, examples for free motion and scattering off a potential barrier are provided, as well as extensions of the concept. We also examine the connection between the dwell time of a quantum particle in a region of space and flux-flux correlations at the boundaries, as well as operational approaches and approximations to measure the flux-flux correlation function and thus the second moment of the dwell time, which is shown to be characteristically quantum, and larger than the corresponding classical moment even for freely moving particles., Comment: To appear in "Time in Quantum Mechanics, Vol. 2", Springer 2009, ed. by J. G. Muga, A. Ruschhaupt and A. del Campo

We examine the connection between the dwell time of a quantum particle in a region of space and flux-flux correlations at the boundaries. It is shown that the first and second moments of a flux-flux correlation function which generalizes a previous proposal by Pollak and Miller [E. Pollak and W. H. Miller, Phys. Rev. Lett. {\bf 53}, 115 (1984)], agree with the corresponding moments of the dwell-time distribution, whereas the third and higher moments do not. We also discuss operational approaches and approximations to measure the flux-flux correlation function and thus the second moment of the dwell time, which is shown to be characteristically quantum, and larger than the corresponding classical moment even for freely moving particles., Comment: 7 pages

We study the effect of quantum motion in a Mach-Zehnder interferometer where ultracold, two-level atoms cross a $\pi/2 $-$\pi $-$\pi/2$ configuration of separated, laser illuminated regions. Explicit and exact expressions are obtained for transmission amplitudes of monochromatic, incident atomic waves using recurrence relations which take into account all possible paths: the direct ones usually considered in the simple semiclassical treatment, but including quantum motion corrections, and the paths in which the atoms are repeatedly reflected at the fields., Comment: 11 pages, 5 figures

We compute the three-loop relation between the pole and the minimally subtracted quark mass allowing for virtual effects from a second massive quark. We also consider the analogue effects for the on-shell wave function renormalization constant., Comment: 24 pages

We study the scattering of two-level atoms at narrow laser fields, modeled by a $\delta$-shape intensity profile. The unique properties of these potentials allow us to give simple analytic solutions for one or two field zones. Several applications are studied: a single $\delta$-laser may serve as a detector model for atom detection and arrival-time measurements, either by means of fluorescence or variations in occupation probabilities. We show that, in principle, this ideal detector can measure the particle density, the quantum mechanical flux, arrival time distributions or local kinetic energy densities. Moreover, two spatially separated $\delta$-lasers are used to investigate quantized-motion effects on Ramsey interferometry., Comment: 11 pages, 5 figures

In this paper we consider the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to three-loop order in perturbation theory. We evaluate the fermionic corrections containing a closed massless fermion loop. The results are building blocks both for the bottom and top quark system at threshold. We explain in detail the methods used for the evaluation of the Feynman diagrams, classify the occurring master integrals and provide results for the latter. The numerical effects are significant. They have the tendency to improve the behaviour of the perturbative series -- both for the bottom and top quark system., Comment: 21 pages

We report a narrowing of the interference pattern obtained in an atomic Ramsey interferometer if the two separated fields have different frequency and their phase difference is controlled. The width of the Ramsey fringes depends inversely on the free flight time of ground state atoms before entering the first field region in addition to the time between the fields. The effect is stable also for atomic wavepackets with initial position and momentum distributions and for realistic mode functions., Comment: 6 pages, 6 figures

We examine the passage of ultracold two-level atoms through two separated laser fields for the nonresonant case. We show that implications of the atomic quantized motion change dramatically the behavior of the interference fringes compared to the semiclassical description of this optical Ramsey interferometer. Using two-channel recurrence relations we are able to express the double-laser scattering amplitudes by means of the single-laser ones and to give explicit analytical results. When considering slower and slower atoms, the transmission probability of the system changes considerably from an interference behavior to a regime where scattering resonances prevail. This may be understood in terms of different families of trajectories that dominate the overall transmission probability in the weak field or in the strong field limit., Comment: 5 figures, 4 pages

We propose and investigate a procedure to measure, at least in principle, a positive quantum version of the local kinetic energy density. This procedure is based, under certain idealized limits, on the detection rate of photons emitted by moving atoms which are excited by a localized laser beam. The same type of experiment, but in different limits, can also provide other non positive-definite versions of the kinetic energy density. A connection with quantum arrival time distributions is discussed., Comment: 13 pages, 1 figures

We provide Standard Model expectations for the rare radiative decays B->K^* gamma, B->rho gamma and B-> omega gamma, and the electroweak penguin decays B->K^* l^+ l^- and B->rho l^+ l^- at the next-to-leading order (NLO), extending our previous results to b->d transitions. We consider branching fractions, isospin asymmetries and direct CP asymmetries. For the electroweak penguin decays, the lepton-invariant mass spectrum and forward-backward asymmetry is also included. Radiative and electroweak penguin transitions in b->d are mainly interesting in the search for new flavour-changing neutral current interactions, but in addition the B->rho gamma decays provide constraints on the CKM parameters (\bar\rho,\bar\eta). The potential impact of these constraints is discussed., Comment: 29 pages, LaTeX

We model ideal arrival-time measurements for free quantum particles and for particles subject to an external interaction by means of a narrow and weak absorbing potential. This approach is related to the operational approach of measuring the first photon emitted from a two-level atom illuminated by a laser. By operator-normalizing the resulting time-of-arrival distribution, a distribution is obtained which for freely moving particles not only recovers the axiomatically derived distribution of Kijowski for states with purely positive momenta but is also applicable to general momentum components. For particles interacting with a square barrier the mean arrival time and corresponding ``tunneling time'' obtained at the transmission side of the barrier becomes independent of the barrier width (Hartman effect) for arbitrarily wide barriers, i.e., without the transition to the ultra-opaque, classical-like regime dominated by wave packet components above the barrier., Comment: 10 pages, 5 figures, RevTex

A recent approach to arrival times used the fluorescence of an atom entering a laser illuminated region and the resulting arrival-time distribution was close to the axiomatic distribution of Kijowski, but not exactly equal, neither in limiting cases nor after compensation of reflection losses by normalization on the level of expectation values. In this paper we employ a normalization on the level of operators, recently proposed in a slightly different context. We show that in this case the axiomatic arrival time distribution of Kijowski is recovered as a limiting case. In addition, it is shown that Allcock's complex potential model is also a limit of the physically motivated fluorescence approach and connected to Kijowski's distribution through operator normalization., Comment: 8 pages, 3 figures, corrected typos

We show -- by explicit computation of first-order corrections -- that the QCD factorization approach previously applied to hadronic two-body decays and to form factor ratios also allows us to compute non-factorizable corrections to exclusive, radiative B meson decays in the heavy quark mass limit. This removes a major part of the theoretical uncertainty in the region of small invariant mass of the photon. We discuss in particular the decays B\to K^* \gamma and B\to K^* l^+l^- and complete the calculation of corrections to the forward-backward asymmetry zero. The new correction shifts the asymmetry zero by 30%, but the result confirms our previous conclusion that the asymmetry zero provides a clean phenomenological determination of the Wilson coefficient C_9., Comment: 34 pages, LaTeX; (v2): reference added, typo in Eq. (93) corrected, Eq. (47) + conventions in Table 1 corrected